The geomorphic significance of step­pools in mountain streams
Anne Chin*
Department of Geography, College of Geosciences, Texas A&M University, College Station, TX 77843-3147, USA
Received 16 April 2002; received in revised form 6 October 2002; accepted 10 March 2003
Abstract
This paper develops a conceptual model to define the changing role and significance of step­pools as energy dissipators in
steep mountain channels. Although energy dissipation is a significant function of step­pools, this role changes over time with
variations in discharge. Steps are effective in reducing stream energy at low flows, but their effectiveness diminishes with
increasing stage. Accordingly, the manner in which energy dissipation occurs also varies. With increasing flows, spill resistance
gives way to a dominance in form and grain resistance. The conceptual model for the changing role of step­pools is illustrated
with data from hydraulic analysis and modeling of step­pools in the Santa Monica Mountains of California. The model points
to the importance of the size of steps in determining their role in energy dissipation and in their interactions with channel
hydraulics. The model offers a new articulation for the geomorphic significance of step­pools in mountain streams, and it
serves as a useful template for a more complete understanding of step­pools over a longer time scale.
D 2003 Elsevier Science B.V. All rights reserved.
Keywords: Step­pool; Energy dissipation; Mountain stream geomorphology
1. Introduction
Steps and pools are ubiquitous bed forms in
mountain stream channels, occurring where gradients
exceed f 2% and materials are in the gravel to
boulder size range (Grant et al., 1990; Montgomery
and Buffington, 1997; Wohl, 2000a). Coarse particles
spanning the channel width create steps (Hayward,
1980), which alternate with finer sediments in pools to
produce a characteristic, repetitive sequence of bed
forms (Chin, 2002) (Fig. 1) with a stepped longitudinal
profile resembling a staircase. The step­pool
morphology similarly develops in bedrock channels
(Duckson and Duckson, 1995, 2001; Wohl, 2000b). In
forested streams, steps are commonly composed of
logs mixed with vegetative debris (Marston, 1982;
Curran and Wohl, in press).
Step­pools serve a fundamental role in river systems
because they provide hydraulic resistance (Abrahams
et al., 1995). Steps induce water to flow over and
through the large roughness elements and plunge into
the pool below, promoting tumbling flow (Peterson and
Mohanty, 1960) where much of the flow's kinetic
energy is dissipated by roller eddies. Steps also cause
a distinct vertical drop in the water surface elevation as
water flows from step to pool. Through vertical fall,
steps decrease the amount of potential energy that
otherwise would be available for conversion to a
longitudinal component of kinetic energy used for
erosion and sediment transport (Ashida et al., 1976;
Marston, 1982). In these ways, steps provide the ability
0169-555X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0169-555X(03)00136-3
* Tel.: +1-979-845-7141; fax: +1-979-862-4487.
E-mail address: chin@tamu.edu (A. Chin).
www.elsevier.com/locate/geomorph
Geomorphology 55 (2003) 125­137
to counterbalance steep gradients, thereby preventing
excessive erosion and channel degradation (Heede,
1981). The role of step­pools is especially important
in confined mountain streams that prohibit lateral
adjustments and energy dissipation by meandering
and braiding (Chin, 1989, 2002).
Despite their common occurrence and functional
importance, step­pools have received little attention in
fluvial geomorphological research compared to riffle­
pools. Recent work has generated important new data
from around the world (e.g., Chartrand and Whiting,
2000; Wohl and Thompson, 2000; Lenzi, 2001; Zimmermann
and Church, 2001; Lee and Ferguson, 2002),
but the specific formative processes are not completely
understood, and the significance of step­pools in the
broader fluvial system has not been fully articulated.
Because upland step­pool channels are linked to
fluvial responses in large downstream basins (Montgomery
and Buffington, 1997) and because step­pool
units are important riparian ecosystems (Scheuerlein,
1999), increased knowledge of step­pools is critical to
the understanding of the overall functioning of the river
system. As urbanization increasingly encroaches upon
mountain fronts in response to population growth
(Chin and Gregory, 2001), improved understanding
of step­pools could also contribute to approaches to
the design and management of steep channels.
This paper develops a conceptual model for the
changing role and significance of step­pools as
energy-dissipating features in the fluvial system.
Although early work has recognized step­pools as
important energy-dissipating mechanisms in steep
slopes (i.e., Heede, 1972; Church and Jones, 1982;
Chin, 1989), this issue could be investigated explicitly,
and the implications for the changing role of
step­pools in the evolution of the fluvial system
could be explored. The role of step­pools changes
over time because the effectiveness of fall obstructions
varies with river stage. Steps are most effective
in reducing stream energy at low flows when vertical
fall is most pronounced. For example, steps account
for 40­100% of the total drop in water surface
elevation in channels of Colorado, Arizona, and
Washington (Heede, 1972, 1981; Curran and Wohl,
in press). However, the effectiveness of energy reduction
by steps is greatly impaired at increasingly high
flows (Heede, 1972; Hayward, 1980; Marston, 1982;
Whittaker and Davies, 1982). Energy loss due to
individual steps is diminished at high flows because
the water surface profile and energy line flatten
(Stuve, 1990; Leopold, 1994; Zimmermann and
Church, 2001) and flow resistance decreases correspondingly
(Beven et al., 1979; Lee and Ferguson,
2002). However, although the importance of documenting
energy dissipation at higher stages has been
recognized (Marston, 1982), critical data have been
lacking to enable a more complete picture of energy
dissipation by step­pools, owing to the difficulties of
Fig. 1. Step­pool sequences in the Santa Monica Mountains, California.
A. Chin / Geomorphology 55 (2003) 125­137126
making process measurements in rugged and often
densely vegetated terrains (Chin, 1989).
The role of step­pools also changes over time
because the manner in which flow resistance is
imparted by steps varies with stage. At low flows,
when the staircase-like step structure is most pronounced
and water plunges from step to pool, spill
resistance is the dominant energy-dissipating mechanism
in step­pool channels (Abrahams et al., 1995),
approaching as much as 80­90% (Curran and Wohl,
in press). However, as stage increases and the step­
pool shape becomes increasingly hidden, spill resistance
gives way to a dominance in form resistance and
then to grain resistance. Thus, the relative dominance
of the energy-dissipating mechanism by steps changes
when considered over time with variations in discharge.
Although the stage-dependency nature of
roughness conditions has been noted (Ergenzinger,
1992; de Jong and Ergenzinger, 1998; Lee and Ferguson,
2002) and attempts at partitioning flow resistance
in step­pool channels during low flow have
been made (Curran and Wohl, in press), further
consideration of energy dissipation over a range of
flows would reveal additional insights for step­pools
over a longer time scale.
Herein, I outline a conceptual model to define the
changing role and significance of step­pools as
energy dissipators in the fluvial system. The model
is built upon answering four specific research questions.
First, how stable are step­pool sequences?
Second, how effective are step­pools in reducing
potential energy through vertical falls? Third, how
does potential energy dissipation vary with increasing
flow? Fourth, at what stage do step­pools become
submerged?
Identifying the points of instability and submergence
are key to the development of the conceptual
model. The point of instability is important because it
marks a change in the fundamental role of steps in the
river system (Chin, 1998). When steps are stable, they
are independent variables that regulate surrounding
flow, channel hydraulics, and energy dissipation; once
steps are mobilized, they become a dependent variable
that adjusts to prevailing flow and energy conditions.
Similarly, the point of submergence marks a major
shift in the dominant role of step­pools in the channel
system, from functioning as fall obstructions that
induce spill resistance, to behaving more like other
bed forms and roughness elements that impart form
and grain resistance. Thus, defining these two points
would form the basis for a model of the changing role
and significance of step­pools in the fluvial system
over a longer time scale. Such a model acknowledges
the progressive development of step­pools in
between large, channel-forming events that break
down the sequences (Lenzi, 2001). This model therefore
applies to step­pool systems that are hydraulically
controlled and capable of being submerged and
restructured at high flows. Examples include the Rio
Cordon of Italy (Lenzi et al., 1997; Lenzi, 2001), the
Lainbach River of Germany (Ergenzinger, 1992;
Gintz et al., 1996), and streams in the Santa Monica
Mountains of the United States (Chin, 1998, 1999a)
where large floods have been observed to submerge
and mobilize steps.
For the remainder of the paper, the term ``energy
dissipator'' is used as in an engineering sense
(Vischer, 1995), in that when a step functions like a
baffle or fall obstruction and induces free water fall, it
is an energy dissipator. However, when a step is
submerged and vertical fall is no longer present, I
will refer to it as a ``roughness elemenť' (Bathurst,
1987). Using this terminology, submergence represents
a point when steps cease to function as energy
dissipators and behave simply as roughness elements
in the stream channel, like any other.
2. Study area and methods
2.1. Theoretical structure
This investigation considers the low flow step­
pool form and process as a middle member of the
range of possible spectrum of states in the evolution of
the fluvial system (Fig. 2). By working backward and
forward from this central state, the channel-forming
flow can be inferred and the effects of the step­pool
morphology on stream energy dissipation can be
determined. Hydraulic reconstructions estimate the
threshold of step­pool mobility; direct field measurements
and hydraulic modeling allow energy dissipation
to be evaluated. Energy dissipation with
increasing flow permits identification of the threshold
discharge at which step­pools become ineffective
energy-dissipating features. Although this threshold
A. Chin / Geomorphology 55 (2003) 125­137 127
discharge does not necessarily have to equal the
channel-forming flow, presumably, at some highmagnitude
flow, the step breaks down and channel
adjustment occurs. Therefore, this theoretical diagram
represents one complete life cycle of a step­pool
sequence, and the task is to define the dimensions
of the diagram.
2.2. Field sites from Santa Monica Mountains
Streams from the Santa Monica Mountains of
southern California are used to define the frequency­magnitude
dimensions of the conceptual
model for the changing role of step­pools. The Santa
Monica Mountains were the site of previous studies
on the stability (Chin, 1998), origin (Chin, 1999a),
morphology (Chin, 1999b), and periodicity (Chin,
2002) of step­pool systems. This analysis uses data
from the hydraulic reconstructions of step­pool mobility
reported in Chin (1998). Thirteen of the original
15 study reaches from Big Sycamore Creek and Cold
Creek are selected for further analysis. These reaches
contain well-developed step­pools. They vary from
0.02 to 0.12 in slope and from 125 to 270 m in length
(Table 1). For more descriptions of the study reaches
and the Santa Monica Mountains, see Chin (1998,
1999a,b, 2002).
2.3. Hydraulic reconstructions
Working backwards from the low-flow state (Fig.
2), hydraulic reconstructions were used to estimate the
high-magnitude flow needed to mobilize steps in the
study reaches. The specific algorithm used was developed
by Costa (1983) for small, steep mountain
streams. A series of computations uses particle size
as the independent variable to determine the velocity
and flow depth necessary to mobilize coarse step
particles:
v  0:18 d 0:487
1
where d is the average size of the five largest
particles (mm) and v is the average velocity (m
s 1
). Depth is determined from a family of equations
that defines Fig. 7 in Costa (1983) (i.e., for
Table 1
Study reaches in the Santa Monica Mountains
Reach Step­
pool
sequences
Length
(m)
Slope
(m/m)
Channel
width
(m)
Step
sizea
(mm)
Cold Creek Preserve 48 186 0.115 2.5 490
Stunt 42 169 0.063 2.5 417
Helsley 45 198 0.038 2.9 313
Bobcat 39 221 0.019 3.2 365
Jude 30 225 0.033 5.6 550
Monte 27 218 0.022 6.6 403
Big Canyon 37 210 0.096 3.5 493
Sycamore Klein 33 170 0.050 2.2 380
Creek Laughlin 29 160 0.047 2.4 405
Scott 38 270 0.061 3.6 519
Bridge 40 190 0.036 5.5 461
Overlook 28 125 0.024 3.6 294
Wood 28 193 0.017 4.7 305
a
Calculated by averaging the b-axis of the five largest rocks
comprising each step.
Fig. 2. Theoretical structure for investigating step­pools. Low flow represents a middle member of the range of possible spectrum of states in
the evolution of the fluvial system.
A. Chin / Geomorphology 55 (2003) 125­137128
slope 0.005, D = 0.012d 0.872
where D is the average
depth (m); for slope 0.010, D = 0.005d 0.788
). Computed
flow depths were evaluated in the field
against high water marks and flood debris, visible
at about half of the study reaches, which suggested
that such depths were reasonable estimates for the
Santa Monica Mountains (Chin, 1999a). Discharge
was computed from cross-sectional surveys and
then related to a flow frequency based on regional
relationships (Young and Cruff, 1967). More background
for this methodology is detailed in Chin
(1998), which also contains the complete set of
data and results for the 15 study reaches in the
Santa Monica Mountains. Threshold discharges
computed with this method are conservative estimates
(Grant et al., 1990; Scheuerlein, 1999; Zimmermann
and Church, 2001) because such factors
as particle imbrication and interaction are unaccounted
for.
2.4. Energy dissipation
An assessment of the significance of step­pools in
stream energy dissipation is to consider potential
energy in a channel reach:
PE  mgh 2
where PE is potential energy; m is mass; g is acceleration
of gravity; and h is height (or elevation) above
a horizontal datum. Thus, PE per unit mass is directly
proportional to height or elevation:
PE=mah 3
Potential energy dissipation caused by steps is the
ratio of the cumulative change of water surface
elevation in vertical falls (h) to the total stream relief,
or change in water surface elevation (Fig. 3):
PE losssteps  h=total stream relief 4
This ratio, commonly used for log steps and organic
debris (e.g., Heede, 1972, 1981; Keller and Swanson,
1979), expresses the potential energy reduced by steps
that otherwise would be available for conversion to
kinetic energy and sediment transport. Marston (1982)
provides more details of energy transformations in
stream channels.
To evaluate potential energy dissipation by step­
pools over a range of flows, the approach was to work
forward from the central low-flow state to the highmagnitude
discharge where steps are submerged and
are no longer effective as energy dissipators (Fig. 2).
This threshold marks the shift from the role of steps in
inducing free water fall to form roughness taking a
greater importance. A series of water surface profiles
were constructed in order to evaluate energy dissipation
and to identify the point of submergence. Field
surveys provided data for the low-flow profile, but
similar data could not be obtained at higher flows.
Fig. 3. Potential energy dissipation by steps.
A. Chin / Geomorphology 55 (2003) 125­137 129
Instead, water surface profiles were modeled for
higher flows using the step-backwater HEC-2 program
of the U.S. Army Corps of Engineers (1990).
2.5. Hydraulic modeling
The HEC-2 model calculates water surface profiles
based on the solution of the one-dimensional energy
equation. It is the original version of HEC-RAS, the
River Analysis System program (U.S. Army Corps of
Engineers, 1998). The newer HEC-RAS model provides
several improved hydraulic features over HEC-2
(Brunner and Piper, 1994), such as alternative channel
subdivision for conveyance calculations and mixed
flow regime calculations, but the two programs are
fundamentally the same. For example, comparison of
water surface elevations calculated with HEC-2 and
those with HEC-RAS at f 2000 cross sections
showed that, for the 10% chance flood, 73.1% of
the cross sections had identical water surface elevations
and 96.9% were within F 0.006 m (Bonner et
al., 1994). Similarly, for the 1% chance flood, 70.1%
of the cross sections showed no difference and 95.8%
were within F 0.006 m.
Because HEC-2 is a one-dimensional model for
steady, gradually varied flow, the assumptions are
difficult to meet for mountain streams. Even so, the
focus on modeling higher flows with HEC-2 in this
application makes the program a reasonable choice.
For example, although HEC-2 often gives inaccurate
predictions of hydraulic parameters during low flows
(Miller and Wenzel, 1985), these errors decline with
increasing stage (Carling and Wood, 1994; Keller and
Florsheim, 1993) because bed-generated turbulence
tends to be less important at higher flows (Jarrett,
1984). Also, although numerous local supercritical
transitions probably occur in step­pool channels,
modeling flow as subcritical nevertheless gives good
results (O'Connor and Webb, 1988) because subcritical
flow has been largely reported for mountain
streams owing to extreme turbulence (Heede, 1972;
Jarrett, 1984; Lopez and Falcon, 1999). Therefore,
because the complex hydraulics associated with
mountain channels are not likely to be represented
fully by any model currently available, simple
hydraulic programs provide useful approximations
for these environments (Lopez and Falcon, 1999).
As a first attempt to model flow through step­pool
channels, HEC-2 allowed another glimpse of highmagnitude
flow conditions where field measurements
were nearly impossible (Keller and Florsheim, 1993;
Carling and Wood, 1994). Similar applications to
pool­riffle reaches (Keller and Florsheim, 1993)
and bedrock channels (Wohl et al., 1999) yielded
good results.
The modeling was performed for a 30-m portion of
Stunt Reach in Cold Creek, 1 of the 13 study reaches
(Fig. 1; Table 1). Seven step­pool sequences comprise
this reach, named Stunt Subreach. The reach is
comparatively simple hydraulically, a desirable trait
for modeling (O'Connor and Webb, 1988). The
accessibility of the reach also facilitates data gathering
for model calibration and verification. Basic input
data for HEC-2 are surveyed channel geometry (cross
sections and length of channel between consecutive
cross sections), initial stage and discharge, flow
regime, and the energy loss coefficients (Manning's
n and expansion/contraction coefficients). A total of
24 surveyed channel cross sections represented Stunt
Subreach; these were taken at every major break in
slope. Five flow profiles were generated; these served
as starting points for indicating trends in energy loss
by steps at higher flows.
The remainder of the paper addresses the four
stated research questions. I then explore the implications
of these findings for the changing role of step­
pools, followed by the development of the conceptual
model outlining the significance of step­pools as
energy dissipators in mountain streams.
3. Mobility, energy dissipation, and the changing
role of step­pools
3.1. Threshold of step mobility
As reported in Chin (1998), results of the hydraulic
calculations indicate that step­pools in the study
reaches of the Santa Monica Mountains are mobilized
by discharges ranging from 0.6 to 295.5 m3
s 1
,
depending on the size of the particles comprising
the steps. The larger the particle sizes, the greater
the flows required. The calculated discharge values
correspond to recurrence intervals of about 2 to 200
years. Thus, for steps consisting of 100- to 200-mm
rocks, movement occurs on the order of 2 to 15 years.
A. Chin / Geomorphology 55 (2003) 125­137130
On the other hand, only the largest steps, composed of
1-m boulders or larger, remain stable for periods of
100 to 200 years. Most steps (median rock size of
about 400 mm) restructure every 15 to 50 years on
average.
These results are applied to Stunt Subreach for
developing the conceptual model for step­pools.
Steps in Stunt Subreach are composed of clast sizes
ranging from 300- to 792-mm. Thus, they are mobilized
by flows with magnitudes ranging from f 7.1
to 43.5 m3
s 1
(Fig. 4), depending on the particle
sizes comprising each step. These critical discharges
correspond to frequencies of about 11 to 62 years in
the Santa Monica Mountains (Chin, 1998). In Fig. 4,
the smallest step (Step A, average 300-mm rocks) and
the largest step (Step B, average 792-mm rocks) are
highlighted for the purpose of illustrating the conceptual
model that follows.
3.2. Energy dissipation at low flow
Potential energy dissipation by step­pools in the
study reaches of the Santa Monica Mountain
streams is nearly complete at low flow (Table 2).
In Cold Creek, steps account for 82­98% of the
total elevation loss in the study reaches (90% for
all reaches combined). Similarly, the cumulative
height of steps nearly equals the total drop in
elevation in the Big Sycamore Creek reaches
(ratio = 80­100%; 97% for all reaches combined).
These values indicate that, through vertical fall,
steps are effective in reducing flow energy that
otherwise might be available for bed and bank
erosion.
Although as a group, steps are effective in
reducing nearly all the elevation losses in study
reaches, a large proportion of the losses are accomplished
by relatively few individuals. For example,
for Stunt Subreach (Fig. 4), Step B alone accounts
for 17.8% of the elevation drops in this reach,
compared to only 1.6% for Step A. Thus, to the
extent that step sizes vary within a given reach,
large steps in the Santa Monica Mountains play
more prominently in potential energy dissipation.
Because in hydraulically controlled reaches such as
those in the Santa Monica Mountains, step height is
dependent upon the particle sizes comprising the
step (Egashira and Ashida, 1991; Chin, 1999b;
Chartrand and Whiting, 2000), potential energy
Fig. 4. Critical flow for initiating motion of step particles, Stunt Subreach, Cold Creek.
Table 2
Potential energy dissipation at low flow
Reach Total
relief
(m)
Cumulative
height of
steps (m)
PE
dissipation
(%)
Cold Creek Preserve 20.88 18.63 89
Stunt 10.43 10.21 98
Helsley 6.63 5.65 85
Bobcat 4.27 3.79 89
Jude 7.35 6.74 92
Monte 4.21 3.47 82
All reaches 53.77 48.49 90
Big Canyon 8.81 7.82 89
Sycamore Klein 7.55 7.38 98
Creek Laughlin 16.02 16.02 100
Scott 20.32 20.12 99
Bridge 6.98 6.83 98
Overlook 2.74 2.19 80
Wood 2.85 2.70 95
All reaches 65.27 63.25 97
A. Chin / Geomorphology 55 (2003) 125­137 131
reduction is expected to vary with step particle size
accordingly.
3.3. Dissipation with increasing flows
Field survey and hydraulic modeling generated
five water surface profiles for Stunt Subreach (Fig.
5). They included the range of flows capable of
mobilizing steps in this reach: 0.05, 0.3, 2.5, 17.63,
and 51.93 m3
s 1
. These discharges correspond to
flow frequencies ranging from < 1 to about 72
years in the Santa Monica Mountains (Chin,
1998). Visual inspection indicates that the low-flow
profile follows the step­pool bed configuration
closely, but the profiles depart with increasing high
flows. The profiles for the two highest flows (17.63
and 51.93 cm) show evidence of the two large
pools only, as the intervening smaller ones are
entirely submerged. This submergence is analogous
to the drowning out of weirs or log jams.
Analysis of the reconstructed water surface profiles
(Fig. 5) shows a trend of decreasing energy losses
with increasing discharge (Table 3). At the low flow
of 0.05 m3
s 1
, because the water surface profile
follows the staircase-like bed configuration closely
and creates a dominant vertical component to the
flow, potential energy dissipation by steps is nearly
complete at 90%. At a flow of 0.30 m3
s 1
, as two of
the smallest steps are drowned out, the remaining
steps are left to account for 81% of the total drop in
water surface elevation in the reach. At 2.5 m3
s 1
,
because submergence occurs for the entire series of
small steps in the central portion of Stunt Subreach,
potential energy dissipation by steps reduces to 67%
(Table 3), attributable to the larger steps only. The
smaller steps, when submerged, therefore become
ineffective as energy dissipators at higher flows.
At the two highest flows, it is unclear whether
vertical drops in the water surface profiles are caused
directly by the steps underneath. This is probably the
case for the discharge of 17.63 cm because flow is
contained within the channel and is insufficient to
mobilize the larger steps in Stunt Subreach (Fig. 4).
The bed profile remains largely intact. However, the
individual large steps contribute to only 27% of the
total loss in water elevation at this flow (Table 3).
On the other hand, the high-magnitude flow of 51.93
cm is best interpreted as flood waves because of the
large depths and flow that spill overbank. According
to the hydraulic calculations (Chin, 1998), a flow of
this magnitude is expected to break down this series
of step­pools in Stunt Subreach (Fig. 4). Thus, not
only are these steps ineffective in energy dissipation
at this discharge, the entire channel bed becomes a
Fig. 5. Water surface profiles from hydraulic modeling.
Table 3
Energy dissipation with increasing flows, Stunt Subreach
Dischargea
(cm)
Total drop
of water surface
elevation (m)
Cumulative drop
of water surface
elevation at steps (m)
PE reduction
by steps (%)
0.05 1.85 1.66 90
0.30 1.66 1.35 81
2.50 1.51 1.01 67
17.63 1.39 0.37 27
a
The discharge of 51.93 cm is not included because a flow of
that magnitude is expected to break down the series of steps in this
reach.
A. Chin / Geomorphology 55 (2003) 125­137132
dependent variable that adjusts to flow and energy
conditions.
3.4. Point of submergence--defining the changing
role of step­pools
When steps are submerged, they lose their distinct
property of inducing vertical fall. More potential
energy is then available for conversion to kinetic
energy and sediment transport; spill resistance gives
way to a dominance in form and grain roughness in
energy dissipation. Thus, at the point of submergence,
steps no longer function as energy dissipators; they
become more like other bed forms and roughness
elements in the channel system. They are analogous to
pool­riffle sequences when submerged.
In Stunt Subreach (Fig. 5), the point of submergence
varies for each individual step because of
variations in their sizes. At the low flow, each of the
seven steps contributes to the total elevation loss in
this reach. Therefore, all individual steps participate as
energy dissipators that induce spill resistance, even
though the extent varies between individual steps
because of varying sizes. As steps become increasingly
drowned at higher flows, an increasing number
of steps cease to function as energy dissipators, and
they increasingly become more like other bed forms in
stream channels. Thus, at the 2.50 cm flow, three of
the smaller steps in the central portion of the reach
become bed forms that impart form and grain roughness.
At the highest flows, only the largest individual
steps remain as energy dissipators. Because large
steps are submerged less frequently, they serve more
prominent roles as energy dissipators over a longer
time scale. For small steps, their role changes readily
when they are drowned during smaller floods.
4. A conceptual model for step­pools
4.1. Toward a general model for step­pools
The point of submergence defined above can be
connected with the channel-forming flow determined
by the hydraulic analysis to develop a conceptual
model describing the function of step­pool systems.
It was originally suggested (Fig. 2) that, as flow
increases and energy dissipation ceases to be effective,
channel restructuring occurs. This general idea
can be refined to consider the two energy-dissipating
mechanisms by steps: potential energy loss through
vertical falls, which approximates spill resistance, and
kinetic energy dissipation by form and grain roughness.
As potential energy reduction diminishes at high
flows (Table 3), energy is available for conversion to
kinetic energy and sediment transport, which become
more important, until flows are sufficient to move
boulders and reform the channel. Thus, a general
model for the significance of step­pools needs to
incorporate the relative dominance of potential and
kinetic energy dissipation. Fig. 6 illustrates this
model, which is an expansion of the right side of
the theoretical diagram of Fig. 2.
4.2. Application to specific test cases
To define its dimensions, the general model is
applied to the two steps highlighted earlier in Stunt
Subreach, Step A and Step B (Fig. 4). They are the
smallest and largest steps in the reach, respectively,
offering greatest contrast. Step A and Step B are
composed of 300- and 793-mm particles, respectively.
Working backward from the low-flow form (Fig.
7A), hydraulic calculations showed that a step of this
size (300-mm) would require flows of about 7.1 m3
s 1
to mobilize. This represents the channel-forming
flow and corresponds to a recurrence interval of about
11 years in Stunt Subreach. Working forward with
increasing discharge, analysis of water surface profiles
indicated that this small step would become submerged
and cease functioning as an energy dissipator
Fig. 6. A general model for energy dissipation by step­pools.
A. Chin / Geomorphology 55 (2003) 125­137 133
at a flow of about 0.3 m3
s 1
, or every year on
average. Therefore, when flow exceeds 0.3 m3
s 1
,
the step behaves more like a roughness element.
Channel hydraulics are analogous to those of pool­
riffle channels and include kinetic energy dissipation
and sediment transport, until flow reaches a critical
magnitude of about 7.1 m3
s 1
. Presumably, at this
point, the step breaks down and reforms, and the
whole cycle begins again.
The same explanation applies for the larger step,
composed of 792-mm rocks (Fig. 7B). The difference is
the relative dominance of potential versus kinetic
energy dissipation. In this case, the larger step has a
longer life span, with restructuring expected to occur
once every 62 years on average in Stunt Subreach.
Because submergence occurs at relatively high flows,
the step behaves as an energy dissipator over a much
larger range of flows and as a roughness element
relatively seldom. Thus, the zone dominated by kinetic
energy dissipation is much smaller.
4.3. A conceptual model for steps of varying sizes
A series of nested diagrams for varying step sizes
results in a conceptual model defining the changing
role of step­pools as energy dissipators (Fig. 8). Each
of the boxes represents a step of a certain size,
arbitrarily chosen from 300- to 800-mm. The time
scale is linear in the diagram, so the length of the box
indicates the average life span for each step. The
vertical dashed lines separate the zones characterized
by potential and kinetic energy dissipation. Therefore,
it identifies the point at which a step makes that
transition, or shift, from functioning as an energy
dissipator to behaving like a roughness element in
the river system.
A point that emerges clearly is how the size of a step
dictates its stability and its role in energy dissipation.
First, the stability of steps obviously depends on their
size as well as flow conditions. Small steps composed
of 300-mm rocks are unstable in comparison, breaking
Fig. 7. Conceptual model for step­pools, Stunt Subreach. (A) 300-mm rocks; (B) 792-mm rocks.
A. Chin / Geomorphology 55 (2003) 125­137134
down every 11 years on average in Stunt Subreach. On
the other hand, large steps on the order of 800 mm are
structures that remain in place for periods of over 60
years. Second, the role of steps in energy dissipation
also changes according to their size. Within their life
spans, the relative dominance of potential energy dissipation
increases with increasing size of the step. This
is clearly shown by the shifting of the dashed lines to
the right within the boxes in Fig. 8, so that large steps
would function as energy dissipators through a large
proportion of the time, whereas small steps would
behave more as roughness elements much of the time.
5. Summary and conclusions
Analysis of step­pools in streams in the Santa
Monica Mountains of California yields answers to the
four stated research questions for this paper and
insights into the significance of step­pools as energy
dissipators in the fluvial system. First, step­pools in
streams in the Santa Monica Mountains are adjustable
bed forms that are capable of being restructured. The
flows required to destabilize step­pool sequences
depend on the particle sizes comprising steps. For steps
in Stunt Subreach, with clast sizes ranging from 300 to
800 mm, these flows have recurrence intervals of about
11 to 62 years. Second, steps are effective energy
dissipators at low flows. Steps account for 80­100%
of the elevation losses in the study reaches in the Santa
Monica Mountains. Through vertical falls, steps reduce
the potential energy that otherwise might be available
for conversion into a longitudinal component of work,
thereby offsetting steep gradients. Third, energy dissipation
by steps diminishes at increasing flows. As
step­pools become increasingly drowned at high
flows, spill resistance gives way to a dominance in
form resistance and, to a lesser extent, grain resistance.
Thus, the manner in which energy dissipation occurs
varies with discharge. Fourth, the point at which steps
become submerged marks a transition in their role as
energy dissipators to roughness elements in the fluvial
system. Because submergence occurs more readily for
small steps, these steps function more as roughness
elements over a longer time scale, whereas large steps
serve more prominent roles as energy dissipators.
These findings permit the development of a conceptual
model that defines the changing role and
significance of step­pools in the larger fluvial system.
The model articulates how the function of step­pools
changes over time with variations in discharge. It also
points to the importance of the step size in determining
its role in energy dissipation and in its interactions with
channel hydraulics. Small steps often function as
roughness elements that impart form and grain roughness,
rather than as energy dissipators that induce spill
resistance. These steps regulate channel hydraulics
comparatively seldom, but they are important as
Fig. 8. Conceptual model for steps of varying sizes.
A. Chin / Geomorphology 55 (2003) 125­137 135
dependent variables that adjust to the prevailing flow
and energy conditions. On the other hand, the role of
energy dissipation becomes primary for large steps.
These steps function predominantly as energy dissipators
during the evolution of the fluvial system. Therefore,
they maintain an independent status throughout
much of the time, regulating and controlling flow and
channel hydraulics.
The model developed in this paper has flow magnitudes
and time dimensions that apply to Stunt Reach in
Cold Creek. However, the model is generally applicable
if frequency­magnitude relations are defined for
other areas and if the boxes and separations in the
model are interpreted as zones rather than clear boundaries.
The model offers a new articulation for the
geomorphic significance of step­pools in mountain
streams, and it serves as a useful template for a more
complete understanding of step­pools over a longer
time scale. Because step­pools characterize mountain
areas that cover a sizable portion of the earth surface,
increased knowledge of step­pools is important in the
broader understanding of mountain geomorphology
and earth surface systems.
Acknowledgements
The Association of American Geographers, Arizona
State University (Office of the Vice President for
Research), and Texas A&M University (Office of the
Vice President for Research) supported portions of the
data collection and analysis contained in this paper. The
following individuals provided critiques to various
drafts of this manuscript and helpful theoretical
discussions: Will Graf (University of South Carolina),
Linda O'Hirok (California State University), Bernie
Bauer (University of Southern California), John
Wolcott (University of Southern California), Doug
Sherman (Texas A&M University), Judy Haschenburger
(University of Auckland), and Ken Gregory
(University of London). Richard Dixon (Southwest
Texas State University) and an anonymous reviewer
made further helpful comments. Lei Wang, Paul
Rindfleisch, and Zengwang Xu (Texas A&M University)
were research assistants; Barbara Trapido-Lurie
(Arizona State University) generously offered technical
expertise. Field assistants are too numerous to
name, but I am grateful to all of them.
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